Second-Order Mass-Weighting\nScheme for Atom-Centered\nDensity Matrix Propagation Molecular Dynamics

The atom-centered density matrix propagation (ADMP) method\nis an\nextended Lagrangian approach to ab initio molecular dynamics, which\nincludes the density matrix in an orthonormalized atom-centered Gaussian\nbasis as additional, fictitious, electronic degrees of freedom, classically\npropagated along with the nuclear ones. A high adiabaticity between\nthe nuclear and electronic subsystems is mandatory in order to keep\nthe trajectory close to the Born–Oppenheimer (BO) surface.\nIn this regard, the fictitious electronic mass <b>μ</b>, being a symmetric, nondiagonal matrix in its most general form,\nrepresents a free parameter, exploitable to optimize the propagation\nof the electronic density. Although mass-weighting schemes in ADMP\nexist, a systematic procedure to define an optimal value of the fictitious\nmasses is not available yet. In this work, in order to rationally\nevaluate the electronic mass, fictitious electronic normal modes are\ndefined through the diagonalization of the Hessian of the electronic\ndensity matrix. If the same frequency is imposed on all such modes\n(compatible with the chosen integration time step), then the corresponding <b>μ</b> matrix can be calculated and then employed for the\nfollowing propagation. Analysis of several ADMP test simulations reveals\nthat such Hessian-based mass-weighting approach is able to ensure,\ntogether with a 0.1/0.2 fs time steps, a high separation between the\n(real) nuclear and the (fictitious) electronic frequencies, which\ndetermines a high adiabaticity. This high, unprecedented, accuracy\nin the propagation leads, in turn, to low errors in the estimated\nnuclear vibrational frequencies, making the ADMP method totally comparable\nto a fully converged BO molecular dynamics simulation but more computationally\nefficient. This work, therefore, contributes to a further development\nof the ADMP ab initio molecular dynamics method, aimed at improving\nits accuracy through a more rational evaluation of the fictitious\nelectronic mass parameter.